Question

If X and Y are two sets such that $X\cup Y$ has 18, X has 8 elements and Y has 15 elements; how many elements does $X\cap Y$ have?

Answer 1

Here

$n(X\cup Y)=18,n\left(X\right)=8$

and $n\left(Y\right)=15$

We know that

$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$

$\therefore$ $18=18+15-n(X\cap Y)$

$\therefore$ $n(X\cap Y)=23-18=5.$